The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
A note on the transitive closure of a boolean matrix
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The row-oriented algorithm in [1] for obtaining transitive closure is Dijkstra's algorithm [2] (for obtaining all nodes reachable from a single node) applied to each row in turn. Furthermore, [1] does not work properly in the acyclic case unless the matrix is in triangular form initially. In general, it may be necessary to renumber the nodes (and correspondingly rearrange the matrix) to bring an acyclic adjacency matrix into triangular form (a technique such as topological sorting [3] can be used). Finally, if interest is in obtaining the nonredundant digraph of an acyclic digraph, [4] appears to be a more efficient algorithm than [5].